Modern Stochastics and Applications

Part I: Probability Distributions in Applications.-Comparing Brownian stochastic integrals for the convex order (Yor, Hirsch).- Application of φ-sub-Gaussian random processes in queueing theory (Kozachenko, Yamnenko).- A review on time-changed pseudo processes and the related distributions (Orsingher).- Reciprocal processes: a stochastic analysis approach (Roelly). Part II: Stochastic Equations.- Probabilistic counterparts of nonlinear parabolic PDE systems (Belopolskaya).- Finite-time blowup and existence of global positive solutions of semilinear SPDE’s with fractional noise (Dozzi, Kolkovska, López-Mimbela).- Hydrodynamics and SDE with Sobolev coefficients (Fang).- Elementary pathwise methods for non-linear parabolic and transport type SPDE with fractal noise (Hinz, Issoglio, Zähle).- SPDE’s driven by general stochastic measures (Radchenko). Part III: Limit Theorems.- Exponential convergence of multi-dimensional stochastic mechanical systems with switching (Anulova, Veretennikov).- Asymptotic behaviour of the distribution density of the fractional Lévy motion (Kulik, Knopova).-Large deviations for random evolutions in the scheme of asymptotically small diffusion (Koroliuk, Samoilenko).- Limit theorems for excursion sets of stationary random fields (Spodarev). Part IV: Finance and Risk.- Ambit processes, their volatility determination and their applications (Corcuera, Farkas, Valdivia).- Some functional analytic tools for utility maximization (Gushchin, Khasanov, Morozov).- Maximization of the survival probability by franchise and deductible amounts in the classical risk model (Ragulina).Part V: Statistics.-Asymptotic properties of drift parameter estimator based on discrete observations of stochastic differential equation driven by fractional Brownian motion ( Mishura, Ralchenko, Seleznev, Shevchenko).- Minimum contrast method for parameter estimation in the spectral domain (Sakhno).- Conditional estimators in exponential regression with errors in covariates (Shklyar).